IJPAM: Volume 26, No. 4 (2006)
-VALUED EXTENSION OF THE FRACTIONAL
MAXIMAL OPERATORS FOR NON-DOUBLING MEASURES
VIA POTENTIAL OPERATORS
MAXIMAL OPERATORS FOR NON-DOUBLING MEASURES
VIA POTENTIAL OPERATORS
Yoshihiro Sawano
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, JAPAN
e-mail: yosihiro@ms.u-tokyo.ac.jp
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, JAPAN
e-mail: yosihiro@ms.u-tokyo.ac.jp
Abstract.In this paper we consider fractional maximal operators with Radon measure on . We do not pose any assumption on the measure except that the measure is non-zero. For the proof we construct Riesz-like potential operators for .
Received: December 5, 2005
AMS Subject Classification: 26A33
Key Words and Phrases: operators for integration and differentiation of fractional order
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 4